Atkin-Lehner |
2+ 5+ 11- 89- |
Signs for the Atkin-Lehner involutions |
Class |
78320k |
Isogeny class |
Conductor |
78320 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
61440 |
Modular degree for the optimal curve |
Δ |
-105428510000 = -1 · 24 · 54 · 113 · 892 |
Discriminant |
Eigenvalues |
2+ 0 5+ -2 11- 0 6 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-298,15747] |
[a1,a2,a3,a4,a6] |
Generators |
[-13:132:1] |
Generators of the group modulo torsion |
j |
-182916347904/6589281875 |
j-invariant |
L |
5.6930120563696 |
L(r)(E,1)/r! |
Ω |
0.88223491816055 |
Real period |
R |
2.1509811568883 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002868 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
39160j1 |
Quadratic twists by: -4 |